Updated July, 2025. Sections of this text were reworded for clarity using LLMs.

Okay folks, following on from Part 2, here’s our third update of the BTC in Eureka post.

– Find part 1 here: https://edu.fair-and-squared.com/BTCBlogPart1
– Find part 2 here: https://edu.fair-and-squared.com/BTCBlogPart2
– Find part 4 here: https://edu.fair-and-squared.com/BTCBlogPart4
Find our free & paid Eureka & BTC resources here: https://edu.fair-and-squared.com/TpTFollow

We’ll wrap up this series next week with the final 4 practices from Building Thinking Classrooms by Peter Liljedahl.
Some points to note:

• After each approach is outlined, we will highlight why that practice is important and beneficial to teachers who use the Eureka curriculum.
• When you see (Liljedahl, 2019), know that I’m referencing information directly from the Building Thinking Classrooms text.
• Those who have implemented the approach, please comment with your thoughts, ideas, and resources.
• The post will take approximately 10 minutes to read. Grab a coffee and enjoy!

– We recommend watching this video to get a snapshot of a Thinking Classroom in real life:

On that note, let’s dive into the next 4 practices to develop a thinking classroom within the Eureka/EngageNY program.

According to him, students need to see homework as something that benefits them, not their teacher. Once that mindset shifts, students are more likely to complete it willingly.

To support this, Liljedahl recommends not checking homework or even asking about it. Save yourself the energy, and save your students and their families the stress. Homework completion should not be your hill to die on.

At this point, I’d like to highlight how I assign homework in my class. I attribute strong MAP score growth in my class to this approach.
Here it is: Implement a flipped classroom and assign Zearn for homework. Students complete the next day’s Zearn lesson for homework the night before. This leaves them ready for the thinking task right from the get-go.

🔴 𝐖𝐡𝐲 𝐢𝐬 𝐭𝐡𝐢𝐬 𝐢𝐦𝐩𝐨𝐫𝐭𝐚𝐧𝐭 𝐟𝐨𝐫 𝐄𝐮𝐫𝐞𝐤𝐚 𝐭𝐞𝐚𝐜𝐡𝐞𝐫𝐬?
Eureka includes homework sheets with each lesson, but let’s be honest — they’re dry and rarely inspiring. In my experience, students often find the answer key online and copy it. That’s a clear sign they view homework as something to please the teacher, not to help themselves.

Zearn, on the other hand, gives students a platform they actually enjoy. It’s trackable, aligned to the lesson, and it prepares them for deeper thinking in class. I tie Zearn completion into my Classroom Economy system: students earn classroom dollars if they choose to complete it.

If you’re aiming to build a love of math in your classroom, skip the worksheet slog. Assign Zearn instead. It’ll save you class time, cut down on homework battles, and set your students up for success.

Quick tip: If your district requires written homework or you’d like to offer extra practice, try using the Eureka-aligned Spiral Review Pack. I typically use it for morning work, but it works just as well as at-home practice.

He points out that “the amount of thinking students were required to do, and did, was sharply reduced in situations where their actions were managed- even micromanaged.” (Liljedahl, 2021).
One of the best ways to avoid micromanaging is by promoting knowledge mobilization. We introduced this concept in Part 1: students move among peer groups to see how others are approaching the thinking task. They return to their own group with new insights, and continue working collaboratively.

While this might sound like it encourages copying, I’ve found the opposite to be true. It leads to some of the most thoughtful, energized group work I’ve ever seen.
Although knowledge mobilization will often occur on its own, it helps when teachers actively direct groups to check in with others. Ask questions like, “Who else is making progress?” or “Whose board has a different strategy?” This light touch can trigger movement, fresh ideas, and deeper thinking.

* Knowledge mobilization is possibly my favorite takeaway from the BTC textbook. The best part of knowledge mobilization is that it will relieve so much of the responsibility on you as the teacher and it will energize your classroom!

🔴 𝐖𝐡𝐲 𝐢𝐬 𝐭𝐡𝐢𝐬 𝐢𝐦𝐩𝐨𝐫𝐭𝐚𝐧𝐭 𝐟𝐨𝐫 𝐄𝐮𝐫𝐞𝐤𝐚 𝐭𝐞𝐚𝐜𝐡𝐞𝐫𝐬?
The Eureka program promotes a highly structured, explicit form of learning. While explicit learning has its merit, it’s “the chili in the dish” where deep learning is the desired outcome. It’s vital to strike a balance between explicit learning and fostering implicit learning experiences in math education. Great math classrooms need both explicit teaching and opportunities for implicit learning. Implicit learning experiences, like those created through knowledge mobility, allow students to explore, discuss, and construct deeper understanding through collaboration.

The introduction of knowledge mobility to your classroom will allow for that implicit learning & deeper conceptual understanding to take place. When we mix the structure of Eureka’s explicit learning with the impliciteness (that’s probably not a real word?!) of the BTC framework, we end up with learners who not only understand mathematical processes, but also build a more meaningful understanding of why those processes work.

To support his point, he references the work of psychologist Mihaly Csikszentmihalyi, who introduced the concept of cognitive flow.
(Check out this video for a great explanation of what “flow” means.)

Cognitive flow is the state where a person is completely absorbed in a task. The nervous system is fully engaged, and the mind is focused without distraction. This state occurs when the level of challenge is just right- not too easy and not too overwhelming.

Because learning is at its strongest during moments of flow, it’s clear that we want our students to enter this state during math tasks.
The question is: how do we help them stay there?

According to Liljedahl, we achieve this by using hints and extensions to adjust the level of challenge as needed. This keeps students engaged, appropriately stretched, and deeply involved in their thinking.

In my classroom, here’s how this plays out in real time:

Hints: When I notice a group struggling, I offer just enough support to help them regain momentum. For example, if a group forgets to carry the one during an addition problem, I might do a quick think-aloud and walk through their process with them. The goal is for them to discover the mistake on their own. Other times, I’ll encourage knowledge mobility by directing them to check out how another group approached the problem correctly.

Extensions: This is where things get exciting. When a group finishes their thinking task ahead of others, I give them an extension that pushes their thinking further. Sometimes the extension connects to a skill we’ve already covered. Other times, it introduces a concept they’ll encounter in an upcoming lesson. Using extensions in this way has allowed us to review past learning in a more meaningful way and to preview future content with surprising success. I’m consistently amazed at what my students can do when challenged just beyond the lesson objective

🔴 𝐖𝐡𝐲 𝐢𝐬 𝐭𝐡𝐢𝐬 𝐢𝐦𝐩𝐨𝐫𝐭𝐚𝐧𝐭 𝐟𝐨𝐫 𝐄𝐮𝐫𝐞𝐤𝐚 𝐭𝐞𝐚𝐜𝐡𝐞𝐫𝐬?
As we discussed in the first post, the heart of the BTC approach is getting students to think. But when tasks are too easy, too difficult, or too dry, students check out. Eureka’s mini-lessons don’t always support that ideal state of engagement known as flow. Hints and extensions help bridge that gap. When used well, they ensure:
• Students stay engaged throughout the entire thinking task.
• Earlier concepts are revisited through active problem-solving.
• Students get a sneak peek at future learning, which builds confidence and curiosity.

One of the most powerful shifts I’ve seen is in students who come in with high math anxiety and little belief in themselves. Through consistent success with thinking tasks and extension challenges, that fear is gradually replaced by confidence. I still remember telling one student, “Guess what? You just mastered tomorrow’s lesson,” and watching their whole face light up. These moments do more than teach content, they reshape identity.

• Show, don’t tell: Start by using student work to introduce the learning objective. Choose one group’s board and annotate directly on it using a different colored marker than what students used. Before offering any explanation, have the class discuss the group’s thinking. Ask questions like:
  “What do you notice?”
  “Did your group get the same answer? Why or why not?”
  “What model did they use?”
• Consolidate from the bottom: Begin with a group that made an error. This approach keeps higher-achieving students engaged by deepening their thinking, while also giving developing learners a place to start consolidating at their own level.
• Get moving: From there, guide the class through the work of one or two other groups, moving from less accurate to more accurate solutions. Ask students to compare, discuss, and reflect on each group’s approach. As Liljedahl notes, “the more steps, the better.” (Liljedahl, 2021)
  
  Keep in mind the following:
• While students work, keep an eye out for the groups you want to highlight during consolidation.
• Let those groups know in advance and remind them not to erase anything. Even if the work contains mistakes, students feel valued when their thinking contributes to class learning.
• Never erase student work without permission. As Liljedahl says, “Erasing devalues their work.”
• Students may still be buzzing from their thinking task. Establish clear expectations to help them stay focused and engaged during this part of the lesson.

🔴 𝐖𝐡𝐲 𝐢𝐬 𝐭𝐡𝐢𝐬 𝐢𝐦𝐩𝐨𝐫𝐭𝐚𝐧𝐭 𝐟𝐨𝐫 𝐄𝐮𝐫𝐞𝐤𝐚 𝐭𝐞𝐚𝐜𝐡𝐞𝐫𝐬?
“If all students could learn by having us just tell them how to do it, we would not have any of the problems that we have in mathematics education today.” (Liljedahl, 2021)
Students don’t want a one-way, 35-minute lecture disguised as a mini-lesson. They want to engage. Inviting them to analyze another group’s work creates far deeper understanding of the concept. As Liljedahl puts it, “Rather than explaining one’s own work, trying to decode someone else’s work changes consolidation from telling to thinking.” (Liljedahl, 2021).

The best part? Once students have attempted the task, you can often explain the Eureka learning objective in under five minutes, right on top of their own thinking. You’ll likely even have time to consolidate an extension or two.

That brings us to the end of our post on Practices 7, 8, 9, and 10 from Building Thinking Classrooms in Mathematics by Peter Liljedahl. We hope this has sparked some fresh ideas for your classroom!

Try the Following This Week — Homework for the Teacher 😎

• Sign up for Zearn and check out the platform.
• Pick two groups and send them to see how another group approached the task.
• Use an extension task with a group that finishes early.
• Send us an email and let us know how it went! info@fair-and-squared.com

Please comment with any responses/thoughts/comments/ideas/questions!

See you soon for Part 4 of Building Thinking Classrooms In The Eureka/EngageNY Program,
The Fair and Squared Team 🌟

To check out all of our free & paid resources, find our TpT store here: https://edu.fair-and-squared.com/TpTstore